You can buy (and should) buy a through ticket from Eurostar. Buying it from Eurostar gives you "CIV protection" - if your first train is delayed and you miss your booked connection you are automatically accommodated on the next train.
Presume you desperately want to go by train? While Eurostar is the sensible choice for London or Brussels, it's much less obvious why you'd pick it for Amsterdam. It's a long journey - most of us would just fly for this route.